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Stark Effect in Rydberg States of Helium and Barium CTW. Lahane STARK EFFECT IN RYDBERG STATES OF HELIUM AND BARIUM STARK EFFECT IN RYDBERG STATES OF HELIUM AND BARIUM Free University Press is an imprint of: VU Boekhandel/Uitgeverij bv De Boelelaan 1105 1081 HV Amsterdam Phone: (0)20-444355 Telex: 18191 vuboe nl isbn 90-6256-750-5 cip nugi 819 © C.T.W. Lahaije, Amsterdam, 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanically, by photocopying, by recording, or otherwise, without prior written permission from the author. VRIJE UNIVERSITEIT TE AMSTERDAM STARK EFFECT IN RYDBERG STATES OF HELIUM AND BARIUM ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Vrije Universiteit te Amsterdam, op gezag van de rector magnificus dr. C. Datema, hoogleraar aan de faculteit der letteren, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de faculteit der natuurkunde en sterrenkunde op woensdag 18 januari 1989 te 15.30 uur in het hoofdgebouw van de universiteit, De Boelelaan 1105 door Christiaan Theodoras Wilhelmus Lahaije geboren te Eindhoven Free University Press Amsterdam 1989 Promotor: prof.dr. W. Hogervorst Referent prof.dr. RP.H. Rettschnick En dan nog iets mijn zoon, een laatste waarschuwing. Er worden te veel boeken geschreven en van al dat lezen wordje alleen maar moe. Prediker 12,12 Aan ....euh, dinges Voorwoord Na bijna vijfjaar is mijn promotie-onderzoek afgerond. Het resultaat, vastgelegd in de vorm van een proefschrift, ligt nu voor u. Geboeid door het fenomeen laser ben ik na mijn af- studeren in 1984 naar Amsterdam gekomen om een promotie-onderzoek aan te vangen op het gebied van laserspectroscopie aan atomen. De afgelopen jaren heb ik benut om mijn kennis op het gebied van lasertechnieken en van de quantummechanica te vergroten. Zoals duidelijk zal zijn ben ik dan ook degene die het meest van deze periode geprofiteerd heeft. Het inspirerend enthousiasme en de goede sfeer binnen de vakgroep atoomfysica zijn mede bepalend geweest voor de succesvolle afronding van mijn promotie-onderzoek. Op deze plaats zou ik dan ook iedereen willen bedanken die heeft bijgedragen aan het tot stand komen van dit proefschrift. Wim Hogervorst, als mijn promotor en directe begeleider was jij degene die het onder- zoek stuurde. Je bood mij echter de vrijheid om experimenten zelf gestalte te geven. Je enthousiasme voor het experiment, je aanstekelijk optimisme en onze wetenschappelijke dis- cussies zijn steeds een stimulans geweest. Je informele manier van werken en ongedwongen persoonlijkheid maakten het mogelijk ten allen tijde voor raad en daad bij je aan te kloppen. Prof. Dr. RJ'Ji. Rettschnick wil ik bedanken voor zijn bereidheid als referent op te wil- len treden. Jacques Bouma, jij vormde samen met Wim Hogervorst de kern van de groep. Dank voor je inventieve bijdragen op het technisch vlak. Onze ontspannende conversaties en jouw relativerende visie op wetenschappers en hun ambities zou ik nooit hebben willen missen. Met Ben Post en Mohamed Zaki Ewiss heb ik de eerste jaren van mijn promotie- onderzoek prettig samengewerkt. Mijn collega's gedurende de gehele promotie-periode waren Wim Vossen en Erwin Bente. In het halfduister van de kelder bracht Wim Vossen mij de beginselen bij van het uitlijnen van een ringlaser; mijn dank hiervoor. Dankbaar heb ik gebruik gemaakt van de door Erwin geschreven besturings- en analyse-programma' s. Tevens wil ik jullie bedanken voor de vele stimulerende wetenschappelijke discussies. Er heeft zich inmiddels een nieuwe generatie promovendi aangediend. Deze groep be- staat momenteel uit Robert de Graajf, Tony van der Veldt, Ilse Aben, Pieternel Levelt en Ger- rit Kuik. Vanaf deze plaats wil ik jullie bedanken voor de (veelal nachtelijke) assistentie die jullie tijdens het experimenteren verleend hebben. Tony van der Veldt in het bijzonder ben ik dank verschuldigd voor zijn medewerking aan de analyses. Wim Ubachs, de nieuwe vaste medewerker in de groep, wil ik bedanken voor het aanleveren van een aantal ideeën voor stel- lingen. Van alle studenten die hebben bijgedragen aan mijn promotie-onderzoek wil ik speciaal Stephen Lorié en Frans van der Meijs bedanken voor de plezierige samenwerking. I thank Dr. K. Sakimoto of the Institute of Space and Astronautical Science in Tokyo for our fruitful discussions concerning the theory of the Stark effect. De heren van de computergroep en van de mechanische en electronische werkplaatsen wil ik bedanken voor hun ondersteuning. Tevens wil ik de heer Pomper bedanken voor het verzorgen van de figuren in dit proefschrift. Werklast en tijdsdruk kenmerken de laatste maanden van een promotie-periode. Het persklaar maken van een proefschrift voor een zekere deadline behoort tot één van de meest zenuwslopende bezigheden van een promotie-onderzoek. Tegen mijn wil in werden sociale contacten verwaarloosd. Ik wil dan ook iedereen in mijn naaste omgeving bedanken voor hun begrip, belangstelling, steun en stimulans. Tenslotte wil ik Anja bedanken voor alle steun en vertrouwen. Contents Chapter 1 Introduction and summary Chapter 2 Theory 9 1. Introduction 9 2. Structure of two electron atoms 9 3. Stark effect in hydrogen 12 4. Stark effect in complex atoms; calculation^ methods 14 4.1 Fcrtubational treatment 16 4.1.1 Spherical base 16 4.1.2 Parabolic base 16 4.1.3 General features 17 4.2 Diagonalisation of the energy matrix 18 4.3 MQDT of the Stark effect 19 4.3.1 Basic outline 19 4.3.2 Basic functions 20 4.3.3 Frame transformation 21 4.3.4 MQDT for quasi-bound Stark states 22 4.3.5 MQDT for autoionizing Stark states 23 4.4 Implementation 26 Chapter 3 Stark manifolds of barium Rydberg states 29 1. Introduction 31 2. Background 32 3. Experimental setup 33 3.1 Atomic beam production and detection 33 3.2 Lasers 33 3.3 Energy values and intensities 33 4. Results and discussion 34 4.1 Determination of quantum defects of higher /-levels 34 4.2 Energy positions of manifold levels 36 4.3 Relative intensity distribution over a manifold 38 5. Conclusions 39 Chapter 4 Electric field induced avoided level crossings in bound Rydberg states of barium 41 1. Introduction 43 2. Experimental setup and results 43 3. Discussion 45 3.1 Theory 45 3 3 3.2 Avoided crossing F2 <-> SX 46 3 x 3.3 Avoided crossing F2 <-> Pi 48 4. Conclusions • 52 Chapters Stark manifolds and electric field induced avoided level crossings in helium Rydberg states 55 1. Introduction 57 2. Theoretical background 58 3. Experimental setup 60 4. Results and discussion 62 4.1 "Isolated" manifolds 62 4.2 Avoided crossings 64 4.2.1 Avoided crossings of two levels of adjacent manifolds 64 4.2.2 Threefold avoided crossings 68 4.3 Remarks 70 5. Conclusions 71 Chapter 6 Electric field effects in weakly autoionizing 5dnf J=5 states of barium 73 1. Introduction 75 2. Theory 76 3. Experimental setup and results 79 3.1 Experimental setup 79 3.2 Experimental results 80 4. Calculational results and discussion 83 4.1 Comparison MQDT method with experimental results 83 4.1.1 Input for MQDT program 83 4.1.2 Comparison between experiment and calculated m=0 spectrum 84 4.1.3 Spectra calculated for I m I = 0,1 and 2 components 86 4.1.4 Avoided crossings between the 5d63d level and n=60 manifold components 87 4.2 MQDT method versus diagonalisation procedure 88 4.3 General remarks 89 5. Conclusions 90 Samenvatting 93 Chapter 3 of this thesis is a reproduction of an article which appeared in "Zeitschrift fur Physik D: Atoms, Molecules and Clusters": Z. Phys. D: At. Mol. Clust. 7 (1987) 37. Chapter 4 is submitted for publication to "Zeitschrift fur Physik D: Atoms, Molecules and Clusters". Chapter 5 is submitted for publication to "Physical Review A". Chapter 6 will be submitted for publication in a slightly revised form. The articles are reproduced with the kind permission of the publishers. Chapter 1 Introduction and summary When a neutral atom is exposed to a static electric field F, its energy levels shift, split and broaden. The shift and splitting effect is usually associated with the name of Stark [1], although Lo Surdo [2] discovered it contemporaneously in 1913 (using a different method). The broadening effect was predicted by Oppenheimer [3] in 1928 to be a tunneling phenomenon and was first observed two years later by von Traubenberg et al. [4]. They meas- ured the quenching of spectral lines of the Balmer series in hydrogen in an electric field. The physics of atoms in external fields is of fundamental interest and is related to the general problem of the properties of isolated atoms in different physical environments [5,6]. Interest for this subject can be found in various fields of physics such as plasma physics [7], astrophysics [8,9,10] and precision time and frequency metrology [11]. Many atomic quantities, such as level energies, fine structure splittings etc., are known to high accuracy and are sensitive probes for external influences. On the other hand, knowledge of the external effects can be used to influence atomic or material processes. As an electric field is easily produced in the laboratory and can be measured precisely, a study of its interaction with isolated atoms (in excited states) is straightforward. Furthermore, from a theoretical point of view the basic atom-field interaction can be evaluated in an essentially exact form. In the past it was only possible to study atoms in their ground state or in low-lying excited states. Under those circumstances external fields are weak compared to the internal atomic fields. It was technically impossible to create laboratory fields which were sufficiently strong to significantly perturb atoms in their normal states.
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